Superposition coding in communications systems shall be described. Multi-user communication systems involve several transmitters and receivers communicating with each other and may use one or more communications methods. In general, multi-user communication methods may be categorized into one of two scenarios:                (a) A single transmitter communicating with several receivers, commonly referred to as a broadcast communications method, and        (b) Several transmitters communicating to a common receiver, which is commonly referred to as a multiple-access communications method.        
The broadcast communications method is commonly known in the communications and information theory literature as the ‘broadcast channel’. The ‘broadcast channel’ refers to each of the physical communication channels between the transmitter and the multiple receivers as well as the communication resources used by the transmitter to communicate. Similarly, the multiple-access communications method is widely known as the ‘multiple-access channel’. The ‘multiple-access channel’ refers to the physical communication channels between the multiple transmitters and the common receiver, along with the communication resources used by the transmitters. The broadcast communications method is frequently used to implement the downlink communication channel in a typical cellular wireless system while the uplink channel in such a system is commonly implemented using the multiple-access communications method.
The transmission resource in a multi-user communication system can generally be represented in time, frequency or code space. Information theory suggests that the capacity of the system can be increased over other communication techniques in both the broadcast scenario and the multiple-access scenario. In particular, by transmitting to multiple receivers simultaneously in the case of the broadcast communications method, or by allowing multiple transmitters to transmit simultaneously in the case of the multiple-access communications method, over the same transmission resource, the capacity of the system can be increased over other communication techniques. In the case of the broadcast communications method, the technique used to transmit simultaneously to multiple users over the same transmission resource is also known as ‘superposition coding’.
The advantages of superposition coding will be apparent in view of the following discussion of transmission techniques for the broadcast communications method. Consider a single transmitter communicating with two receivers, whose channels can be described by ambient Gaussian noise levels of N1 and N2, with N1<N2, i.e., the first receiver operates over a stronger channel than the second receiver. Assume that the communication resources available to the transmitter are a total bandwidth of W, and a total power of P. The transmitter may employ several strategies to communicate with the receivers. FIG. 1 is a graph 100 plotting the achievable rates in a broadcast channel for a first and second user for three different transmission strategies. Vertical axis 102 represents the rate for the stronger receiver, while horizontal axis 104 represents the rate for the weaker receiver. Line 106 shows achievable rates for a time division multiplexing (TDM) strategy. Line 108 shows achievable rates for a frequency division multiplexing (FDM) strategy. Line 110 shows maximum capacity achievable rates.
First, consider the strategy where the transmitter multiplexes between the two receivers in time, allocating all its resources to one receiver at a time. If the fraction of time spent communicating with the first (stronger) receiver is denoted by α, it may be shown that the achievable rates for the two users satisfy the following equations.
            R      1        ≤          α      ⁢                          ⁢      W      ⁢                          ⁢              log        ⁡                  (                      1            +                          P                              N                1                                              )                      ,          ⁢            R      2        ≤                  (                  1          -          α                )            ⁢      W      ⁢                          ⁢              log        ⁡                  (                      1            +                          P                              N                2                                              )                    
As the fraction of time spent serving the first user, α, varies, the rates achieved by the above equations are represented with the straight solid line 106 corresponding to ‘TDM’ as shown in FIG. 1.
Now consider a different transmission strategy where the transmitter allocates a certain fraction of the bandwidth, β, and a fraction of the available power, γ, to the first user. The second user gets the remaining fractions of bandwidth and power. Having allocated these fractions, the transmitter communicates with the two receivers simultaneously. Under this transmission strategy, the rate region can be characterized by the following equations.
            R      1        ≤          β      ⁢                          ⁢      W      ⁢                          ⁢              log        ⁡                  (                      1            +                                          α                ⁢                                                                  ⁢                P                                            N                1                                              )                      ,          ⁢            R      2        ≤                  (                  1          -          β                )            ⁢      W      ⁢                          ⁢                        log          ⁡                      (                          1              +                                                                    (                                          1                      -                      α                                        )                                    ⁢                  P                                                  N                  2                                                      )                          .            
The rates achieved by the above equations are visualized intuitively from the convex dashed curve line 108 corresponding to ‘FDM’ as shown in FIG. 1. It is evident that the strategy of dividing the available power and bandwidth between the two users in an appropriate manner outperforms the time-division partition of resources. However, the second strategy, is not yet the optimal one.
The supremum of the rate regions achievable under all transmission strategies is the broadcast capacity region. For the Gaussian case, this region is characterized by the equations
            R      1        ≤          W      ⁢                          ⁢              log        ⁡                  (                      1            +                                          α                ⁢                                                                  ⁢                P                                            N                1                                              )                      ,          ⁢            R      2        ≤          W      ⁢                          ⁢              log        ⁡                  (                      1            +                                                            (                                      1                    -                    α                                    )                                ⁢                P                                                              α                  ⁢                                                                          ⁢                  P                                +                                  N                  2                                                              )                      ,and is indicated by the dash/dot curve line 110 corresponding to ‘CAPACITY’ as shown in FIG. 1.
It was shown by Thomas Cover in T.M. Cover, Broadcast Channels, IEEE Transactions on Information Theory, IT-18 (1): Feb. 14, 1972, that a communication technique called superposition coding could achieve this capacity region. In this technique, the signals to different users are transmitted with different powers in the same transmission resource and superposed on each other. The gains achievable through superposition coding surpass any other communication technique that requires splitting of the transmission resource among different users.
The basic concept of superposition coding is illustrated in FIG. 2. FIG. 2 is a graph 200 illustrating a high power QPSK signal and a low power QPSK signal superposed on the high power QPSK signal. Vertical axis 202 represents Q-component signal strength while horizontal axis 204 represents P-component signal strength. While the example of FIG. 2 assumes QPSK modulation, the choice of modulation sets is not restrictive, and, in general, other modulation sets may be alternatively used. Also, the example FIG. 2 is sketched out for an exemplary case of two users, while the concept may be generalized and applied in a straightforward manner to multiple users. Assume that the transmitter has a total transmit power budget P. Suppose that the first receiver, referred to as ‘weaker receiver’, sees larger channel noise and the second receiver, referred to as ‘stronger receiver’, sees smaller channel noise. Four circles 206, filled in with a pattern, represent the QPSK constellation points to be transmitted at high power (better protected), (1−α)P, to the weaker receiver. Meanwhile, additional information is conveyed to the stronger receiver at low power (less protected), αP, also using a QPSK constellation. In FIG. 2, arrow 208 of magnitude √((1−α)P) provides an indication of the high transmission power, while arrow 210 √(αP) provides an indication of the low transmission power. The actually transmitted symbols, which combine both the high power and low power signals, are represented as blank circles 212 in the figure. A key concept that this illustration conveys is that the transmitter communicates to both users simultaneously using the same transmission resource.
The receiver strategy is straightforward. The weaker receiver sees the high power QPSK constellation with a low-power signal superposed on it. The SNR experienced by the weaker receiver may be insufficient to resolve the low-power signal, so the low power signal appears as noise and slightly degrades the SNR when the weaker receiver decodes the high power signal. On the other hand, the SNR experienced by the stronger receiver is sufficient to resolve both the high power and low power QPSK constellation points. The stronger receiver's strategy is to decode the high-power points (which are intended for the weaker receiver) first, remove their contribution from the composite signal, and then decode the low-power signal.
Based upon the above discussion, it should be appreciated that there is a need for variations and/or adaptations of the superposition coding concept which could be used to more effectively utilize air link resources in broadcast and/or multiple-access communications systems. In a wireless communications system, with multiple users, at any given time, different channel qualities will exist for the various users. Methods and apparatus that characterize the different receivers and transmitters as weaker/stronger on a relative basis with respect to one another and allow for these relative classifications to change over time may also be useful. Methods and apparatus of scheduling and power control that opportunistically utilize these differences and apply superposition coding methods could increase system capacity. New implementations using superposition coding methods may need methods to convey information between transmitters(s) and receiver(s) concerning the superposition coding, e.g., such as the temporary weaker/stronger assignment information. Methods of communicating such information that minimize overhead, where possible, and/or combine or link temporary assignment designations between multiple communication channel segments, e.g., an assignment channel segment and a traffic channel segment, would be advantageous.